Whence then, one will say, does their opacity come?  Is it because the particles which compose them are soft; that is to say, these particles being composed of others that are smaller, are they capable of changing their figure on receiving the pressure of the ethereal particles, the motion of which they thereby damp, and so hinder the continuance of the waves of light?  That cannot be:  for if the particles of the metals are soft, how is it that polished silver and mercury reflect light so strongly?  What I find to be most probable herein, is to say that metallic bodies, which are almost the only really opaque ones, have mixed amongst their hard particles some soft ones; so that some serve to cause reflexion and the others to hinder transparency; while, on the other hand, transparent bodies contain only hard particles which have the faculty of recoil, and serve together with those of the ethereal matter for the propagation of the waves of light, as has been said.

[Illustration]

Let us pass now to the explanation of the effects of Refraction, assuming, as we have done, the passage of waves of light through transparent bodies, and the diminution of velocity which these same waves suffer in them.

The chief property of Refraction is that a ray of light, such as ab, being in the air, and falling obliquely upon the polished surface of a transparent body, such as FG, is broken at the point of incidence B, in such a way that with the straight line DBE which cuts the surface perpendicularly it makes an angle CBE less than ABD which it made with the same perpendicular when in the air.  And the measure of these angles is found by describing, about the point B, a circle which cuts the radii ab, bc.  For the perpendiculars ad, CE, let fall from the points of intersection upon the straight line de, which are called the Sines of the angles ABD, CBE, have a certain ratio between themselves; which ratio is always the same for all inclinations of the incident ray, at least for a given transparent body.  This ratio is, in glass, very nearly as 3 to 2; and in water very nearly as 4 to 3; and is likewise different in other diaphanous bodies.

Another property, similar to this, is that the refractions are reciprocal between the rays entering into a transparent body and those which are leaving it.  That is to say that if the ray ab in entering the transparent body is refracted into bc, then likewise CB being taken as a ray in the interior of this body will be refracted, on passing out, into Ba.

[Illustration]